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All right machin uppers Here we go Another question Foreign

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triangle's Two sides of a triangle are known These two

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sides measure thirteen and eighteen units Which of the following

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could not be the perimeter of the triangle So let's

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think about it But we have a line thirteen long

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here and it's connected here and there's Another one's eighteen

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so hung time take out the triangle inequality serum We

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aren't given the length of the third side of the

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triangle but using that to given sides allows us to

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find a range of possible lengths for the third leg

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The triangle inequality Throughem tells us that given to sides

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they envy of the triangle is less than be the

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third side Must be between b minus a and b

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plus eh Right So well see why this is true

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Imagine the angle between a and b is very small

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In that case vienna are almost on top of each

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other Almost looks like a thick line The third side

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that connects them can't be shorter than be minus a

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well The other extreme All the angle between a and

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b is very large Say close to one hundred eighty

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degrees and if that's the case then the third side

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that connects them can't be longer than b plus eh

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So we have two sides of the triangle and we

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know the third side must have a length Between well

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eighteen minus thirteen is five units or well eighteen plus

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thirteen is thirty one units Interesting So if the third

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side fell out of this range we would not be

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able to connect the three sides to actually make a

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triangle It'd be other too short or too long Well

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given that the third side must measure between five and

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thirty one units the perimeter of the entire triangle must

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be between thirteen plus eighteen plus five that's thirty six

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units and sixty two units We have thirteen plus eighteen

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thirty one right well the only answer choice that lives

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outside this ranges eh thirty five units So that's the 00:01:50.536 --> [endTime] answer for shmoop

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